Complex product structures on Lie algebras
By Adrián Andrada, S. Salamon. 2003
115 citations recorded by the source corpus.
Abstract A study is made of real Lie algebras admitting compatible complex and product structures, including numerous 4-dimensional examples. Any Lie algebra ɡ with such a structure is even-dimensional and its complexification has a hypercomplex structure. In addition, ɡ splits into the direct sum of two Lie subalgebras of the same dimension, and each of these is shown to have a left-symmetric algebra (LSA) structure. Interpretations of these results are obtained that are relevant to the theory of both hypercomplex and hypersymplectic manifolds and their associated connections.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f3e3fa33b63679fde289a9dff63be40e99730a78
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In Algebra and Number Theory
In Geometry and Topology
- G. Ovando
- Adrián Andrada
- M. L. Barberis
- I. Dotti
- Dmitri Alekseevsky
- C. Medori
- Adriano Tomassini
- Anna Fino
In Mathematical Physics
- G. Ovando
- Adrián Andrada
- M. L. Barberis
- I. Dotti
- Dmitri Alekseevsky
- C. Medori
- Adriano Tomassini
- S. Salamon
Citations in the corpus
- PRODUCT STRUCTURES ON FOUR DIMENSIONAL SOLVABLE LIE ALGEBRAS (2004, methodology): “of g + and g− where g− is an ideal of g, that is, there is a split exact sequence 0 −→ g− −→ g−→ g + −→ 0. Product structures or, equivalently, double Lie algebras, were used in several contexts (see [AS], [LW]). Important examples of double Lie algebras are Manin triples and complex product structu”
- Homogeneous para-Kähler Einstein manifolds (2009, background): “It is proved in [26] that the Lie algebras g± carry the structure of left-symmetric algebras (Vinberg algebras).”